NFL Passer Rating

12:22 Tue 12 Jan 2010
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In 1973 the NFL adopted a new way of measuring statistical passer performance. The passer rating system attempts to combine various aspects of the passing game into one metric.

The four components it uses are:

  • Pass completion percentage.
  • Average yards per attempt.
  • Touchdown pass percentage.
  • Interception percentage.

Those are all fairly reasonable things to include. One could argue with them, or claim that sacks should also be considered, or make a number of other tweaks, but those four statistics are fairly logical.

The system uses historical averages for each of those statistics to determine how they should be measured. That makes sense, somewhat more sense than a cruder methodology—for example, if you convert completion percentage straight over, the differences would be fairly small, as The difference between 85% completion and 71% completion, 14%, would get reduced to a quarter of that when combined with the other three measures, which seems off since 85% is a completely ridiculous number and should be rated very highly. So the formula for that component is weighted so that 70% is the threshold for “exceptional” for completion percentage. The other components have their own standards, similarly based on historical performance.

Here are the formulas for each component of passer rating:

  • Pass completion: .05 X ((100 X completions/attempts) -30)
  • Average yards: .25 X ((total pass yards/attempts)-3)
  • Touchdowns: 20 X (touchdowns/attempts)
  • Interceptions: 2.375 – (25 X interceptions/attempts)

These are all capped at 2.375 (and cannot go below zero).

That’s all fine. Some of the methodology used is a little tricky, but there may be great reasons for that which I don’t understand.

However, the NFL made the fairly bizarre decision to make the upper limit for each component 2.375. That seems insane, but again, maybe some complex weighting factors meant that this number was the only one that would work. I have my doubts, but it’s possible. Some of the numbers are clearly quite arbitrary (why 25 times interception percentage?); one has to assume that these numbers come out of historical analysis.

This produces four factors contributing a maximum of 2.375 and a minimum of zero, or a scale that goes from 0–9.5.

9.5 is an awkward number, but that’s not a major challenge. Clearly the thing to do here is to simply multiply by 100 and divide by 9.5, producing an easily-comprehensible percentage.

However that’s not what they chose to do. Instead, they multiply by 100 and divide by six, producing… a number that requires explanation every time it’s used. Almost every article I’ve seen that mentions a quarterback’s passer rating goes on then state what the maximum is (158.3), because it’s just unclear what the number means otherwise. Even with that information, it’s not entirely clear.

I just find it difficult to comprehend the decision to make an arbitrary scale max out at 158.3. I understand that they wanted to have a rating of 100 mean something specific, to be the threshold between a good performance and an exceptional one, but the problem is that the numbers that people see are the actual ratings, and not the threshold, so making the threshold neat and friendly is almost useless. The threshold is also arbitrary, and is only going to be studied by people who are really stats geeks (e.g. analysts attempting to discern a quarterback’s eligibility for the Hall of Fame), and so that’s a number that could be safely bizarre (like 63.157894%, which is approximately what a passer rating of 100 becomes if you shift the system to a straight percentage).

This really comes down to a usability issue. If this major statistic needs to be explained every time it’s used, that’s a significant failing. Compare the following two sentences:

Warner finished with a 154.1 rating (158.3 is perfect).

Warner finished with a 97.33% rating.


Warner and Rodgers were both excellent, with ratings of 154.1 and 121.3 (158.3 is perfect).

Warner and Rodgers were both excellent, with ratings of 97.33% and 76.61%.

The percentage is far easier to understand. Even when the maximum is provided, it’s not easy for us to simply eyeball the rating against the 158.3 maximum. Nor is it easy to compare ratings, whereas we’re quite used to comparing percentages.

There is one argument (apart from inertia) for keeping the current system: its strangeness makes necessary some deciphering work, and that work makes it more likely that the user will have some idea of what the thresholds for passer performance are. I don’t think that’s a good enough argument, and think that anyone interested would find those statistics themselves.

I converted Warner and Rodgers’ numbers from yesterday using the quick approach of multiplying by 6 and dividing by 9.5, but the more accurate approach would be to go from the individual components:



Completion %

88%, becomes 2.375

66%, becomes 1.83

Average Yards

11.48, becomes 2.12

10.047, becomes 1.76

TD %

15.15%, becomes 2.375

9.5238%, becomes 1.90


0%, becomes 2.375

2.38%, becomes 1.779




NFL rating



% rating



I’m quite convinced that a straight percentage would simply be a lot better all around.

Note that this alteration would make comparisons with the old formula quite easy, and that it doesn’t rebalance the components in any way. All it does is remove the arbitrary division by six and replace it with a rather more sensible (in this case) 9.5.

There are arguments for using an entirely different system. See for example this “replacement value” approach.

Incidentally, I particularly like how the official NFL page on the passer rating formula makes a point of calling out the fact that it’s a passer rating and not a quarterback rating, that it’s purely statistical and doesn’t measure leadership, play-calling, or other “intangibles”–but the title of the page is “QB Rating Calc – Help”, the header reads “NFL Quarterback Rating Formula”, and the URL is http://www.nfl.com/help/quarterbackratingformula

One Response to “NFL Passer Rating”

  1. Stephen Casey Says:

    I’ve not come across the stat before, I have to admit, I tend to tune out into a bemused inner dialogue that mocks the fact that someone thinks it worth mentioning that a particular player has now become the third best in NFL history for games in which they’ve had multiple sacks (Dumervil of the Broncos).

    However, from your description it appears to me that it was designed as a stat that would enable a viewer to see that a quarterback was ahead of the game as a result of having a 110 point score. Communicating the same information via a stat would require the sentence, “Josh Johnson has a rating of 55% which is below the average of 63.17%”. Combined with the same mechanism for rating every position, viewers would become familiar with the system and get more useful information, more easily.


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